Finite Group Databasebeta

← #28402303

Subgroups — #28402303

Order 14464.

494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813643C212yesmaximal, complemented
2#20299268C211yesmaximal, characteristic, complemented
3#20299251C211yesmaximal, characteristic, complemented
4#20298824C212yesmaximal, complemented
5#20298805C211yesmaximal, characteristic, complemented
6#20298790C211yesmaximal, characteristic, complemented
7#20298757C212yesmaximal, complemented
8#20298742C212yesmaximal, complemented
9C4×#14268636C211yesmaximal, characteristic, complemented
10C8×D452C211yesmaximal, characteristic, complemented
11#492×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2212yes—
13C2×#14268646C2212yes—
14#16813643—28no—
15C2×#14268637C2212yes—
16C2×#14268636C2211yescharacteristic
17C2×#14268632C2212yes—
18C2×C8×D113C2212yes—
19#16813618—21no—
20#16813607—22no—
21#16813598C2212yes—
22#16813597—21no—
23#16813594—22no—
24#16813593C2212yes—
25C4×Dic226C2211yescharacteristic
26C4×D452C2211yescharacteristic
27C4×D452C2211yescharacteristic
28D4×Dic113—21no—
29C4⋊C4×D113—21no—
30#16813554C2211yescharacteristic
31C4⋊#11744751C2211yescharacteristic
32#16813547C2211yescharacteristic
33#16813546C2212yes—
34#16813544C2211yescharacteristic
35#16813543C2212yes—
36#16813534C2212yes—
37C2×SD16×C113C2212yes—
38C2×SD16×C113C2212yes—
39C4⋊Q8×C113C2211yescharacteristic
40#127×C113C2211yescharacteristic
41C4×C8×C113C2211yescharacteristic
42#14268648—24no—
43#14268648—42no—
44#14268646—24no—
45#14268646—42no—
46C2×Dic226C2311yescharacteristic
47C2×D452—22no—
48C2×D452D411yescharacteristic
49C2×D452C2311yescharacteristic
50C2×C22⋊D113—22no—
51C2×C22⋊D113—22no—
52C22×Dic113—22no—
53C2×C4×D113—21no—
54C2×C4×D113—22no—
55C2×C4×D113C2312yes—
56#14268637—24no—
57#14268636D414yescomplemented
58#14268632—24no—
59C2×#11744751C2312yes—
60C8×D113—24no—
61C4⋊Dic113D411yescharacteristic
62C4⋊Dic113C2311yescharacteristic
63C4⋊Dic113C2311yescharacteristic
64#14268626—21no—
65#14268626—22no—
66C22⋊Dic113—22no—
67#14268624—22no—
68#14268624—21no—
69#14268624D412yes—
70C4×Dic113—21no—
71C2×Q8×C113C2312yes—
72C2×D4×C113—21no—
73C2×D4×C113—21no—
74C2×D4×C113C2312yes—
75SD16×C113—24no—
76SD16×C113—42no—
77C2×C8×C113C2311yescharacteristic
78C2×C8×C113C2311yescharacteristic
79C4⋊C4×C113—21no—
80C4⋊C4×C113—21no—
81C42×C113C2311yescharacteristic
82C23×C113—22no—
83C22×D113—21no—
84C22×D113C2×D412yes—
85Q8×C113—22no—
86Q8×C113—22no—
87D4×C113—22no—
88D4×C113—22no—
89D4×C113—42no—
90D4×C113—81no—
91C2×C4×C113—22no—
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2411yescharacteristic
95C22⋊D113—44no—
96C22⋊D113—82no—
97C2×Dic113—21no—
98C2×Dic113—21no—
99C2×Dic113—21no—
100C2×Dic113—44no—
101C2×Dic113C2×D412yes—
102D452—22no—
103D452—21no—
104D452—44no—
105D452C2×D412yes—
106C4×D113—22no—
107C4×D113—22no—
108C4×D113—44no—
109C4×D113—42no—
110Dic226—21no—
111Dic226C2×D412yes—
112C8×C113—21no—
113C8×C113C2×D412yes—
114#11744751—22no—
115C22×C113—42no—
116C22×C113—42no—
117C22×C113—42no—
118C22×C113C22×D411yescharacteristic
119C2×D113—22no—
120C2×D113—22no—
121C2×D113—22no—
122C2×D113—22no—
123C2×D113—41no—
124C2×D113—41no—
125C4×C113—21no—
126C4×C113—42no—
127C4×C113#13512yescomplemented
128C4×C113C22×D411yescharacteristic
129C4×C113H(5,𝔽2)11yescharacteristic
130Dic113—22no—
131Dic113—22no—
132Dic113—41no—
133Dic113—41no—
134C2×C113—82no—
135C2×C113D4211yescharacteristic
136C2×C113C2×#13511yescharacteristic
137C2×C113#57711yescharacteristic
138D113—42no—
139D113—42no—
140#3284—1131nomaximal, Sylow
141C113#328411yescharacteristic, complemented, Sylow
142C2×#135—1132no—
143#550—1131no—
144#547—1131no—
145#492D11311yescharacteristic, complemented
146#465—1132no—
147#462—1131no—
148#459—1131no—
149#452—1132no—
150#449—1132no—
151C4×SD16—1131no—
152C8×D4—1131no—
153C2×#41—1132no—
154C2×#41—1132no—
155#135—2268no—
156C2×Q16—1132no—
157C2×SD16—1131no—
158C2×SD16C2×D11312yes—
159C2×SD16C2×D11312yes—
160C2×D8—1132no—
161C22×C8—1132no—
162C4⋊Q8C2×D11311yescharacteristic
163#127—2261no—
164#127C2×D11311yescharacteristic
165#123—2262no—
166C22⋊Q8—1132no—
167#121—1132no—
168#121—2262no—
169#121—2261no—
170C4×Q8—1131no—
171C4×D4—1131no—
172C4×D4—1131no—
173C4×D4—2261no—
174C2×C4⋊C4—2261no—
175#106—1131no—
176C4⋊C8—1131no—
177#103—1132no—
178#103—1131no—
179#102—1132no—
180#102—1131no—
181C22⋊C8—1132no—
182C4×C8C2×D11311yescharacteristic
183#41—4522no—
184#41—4522no—
185#41—2264no—
186#41—2264no—
187C2×Q8—1131no—
188C2×Q8C22×D11312yes—
189C2×D4—21no—
190C2×D4—21no—
191C2×D4—1131no—
192C2×D4—1131no—
193C2×D4—2262no—
194C2×D4—2262no—
195C2×D4—2262no—
196C2×D4C22×D11312yes—
197C22×C4—1132no—
198C22×C4—2262no—
199C22×C4—2262no—
200C22×C4—2261no—
201Q16—2264no—
202SD16—24no—
203SD16—42no—
204SD16—1134no—
205D8—2264no—
206C2×C8—1132no—
207C2×C8—2264no—
208C2×C8C22×D11311yescharacteristic
209C2×C8C22×D11311yescharacteristic
210C4⋊C4—21no—
211C4⋊C4—21no—
212C4⋊C4—1131no—
213C4⋊C4—1131no—
214C4⋊C4—1131no—
215C4⋊C4—2262no—
216C4⋊C4—2261no—
217C22⋊C4—1132no—
218C22⋊C4—2262no—
219C22⋊C4—2262no—
220C22⋊C4—2261no—
221C42—2261no—
222C42C22×D11311yescharacteristic
223C23—22no—
224C23—1132no—
225C23—2261no—
226Q8—22no—
227Q8—22no—
228Q8—1132no—
229Q8—2261no—
230D4—22no—
231D4—22no—
232D4—42no—
233D4—81no—
234D4—1132no—
235D4—9042no—
236D4—4524no—
237D4—4524no—
238D4—2262no—
239D4—2261no—
240C2×C4—22no—
241C2×C4—1132no—
242C2×C4—4524no—
243C2×C4—4522no—
244C2×C4—4524no—
245C2×C4—2261no—
246C2×C4—2261no—
247C2×C4—2261no—
248C2×C4—2262no—
249C2×C4—2262no—
250C2×C4D4×D11311yescharacteristic
251C2×C4D4×D11311yescharacteristic
252C2×C4C23×D11311yescharacteristic
253C8—21no—
254C8—2262no—
255C8D4×D11312yes—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—4521no—
260C22—4521no—
261C22—2262no—
262C22—2262no—
263C22—2262no—
264C22—2262no—
265C22C2×D4×D11311yescharacteristic
266C4—21no—
267C4—42no—
268C4—4521no—
269C4—4521no—
270C4—2262no—
271C4—2262no—
272C4#1681364312yescomplemented
273C4C2×D4×D11311yescharacteristic
274C4#1681366711yescharacteristic
275C2—82no—
276C2—4522no—
277C2—4522no—
278C2#2029923311yescharacteristic
279C2C2×#1681364311yescharacteristic
280C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#492×C113C2
socleC22×C113C22×D4
hypercenter#492D113
hypocenterC113#3284
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16813643C2semidirect
2. #20299268C2semidirect
3. #20299251C2semidirect
4. #20298824C2semidirect
5. #20298805C2semidirect
6. #20298790C2semidirect
7. #20298757C2semidirect
8. #20298742C2semidirect
9. C4×#14268636C2semidirect
10. C8×D452C2semidirect
11. #492×C113C2semidirect
57. #14268636D4semidirect
127. C4×C113#135semidirect
141. C113#3284semidirect
145. #492D113semidirect
272. C4#16813643semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168136432
#202992682
#202992512
#202988242
#202988052
#202987902
#202987572
#202987422
C4×#142686362
C8×D4522
#492×C1132
#3284113